Due to the limited spatial resolution and partial volume effects of positron emission tomography (PET), and, to a lesser extent, of Magnetic Resonance Imaging (MRI), most tissue regions studied with these imaging modalities are heterogeneous with respect to the physiological and/or biochemical processes being examined and with respect to the concentrations of the relevant labeled compounds in the tissue. Most quantitative work up to now has made the simplifying assumption that the tissues are homogeneous; this has led not only to inaccurate quantification, but also to serious misinterpretations of results in some studies. We have studied the effects of tissue heterogeneity on determination of local cerebral glucose utilization and local cerebral blood flow. Mathematical models to describe the kinetics of deoxyglucose or fluorodeoxyglucose uptake and metabolism in heterogeneous tissues were developed and validated in simulation, animal, and human studies. The most appropriate kinetic model and optimal experimental protocol for the measurement of cerebral glucose utilization in man with [F-18]fluorodeoxyglucose and PET were identified. New tools were developed and optimized for the analysis of time-series data from tracer studies. These tools facilitate the construction of kinetic models of new tracers and the extension of mathematical models of currently-used tracers to additional physiological and pathophysiological conditions. We have optimized and established the properties of a new spectral analysis technique that differs from conventional analyses in that it does not rely on the a priori postulation of a kinetic model nor on the assumption of tissue homogeneity. We have also validated the spectral analysis technique to multiexponential models, e.g. those for clearance of radiotracers from the plasma. We have developed a new robust method for parameter estimation and hypothesis testing that doe snot depend on the statistical distribution of the measured data.